S-wave Superconductor Research Articles

Perfect modulation between fully spin-polarized spin-singlet and -triplet Andreev entanglements in a narrow quantum spin Hall system

We consider a quantum spin Hall (QSH) insulator strip touching on one s-wave superconductor sandwiched between two ferromagnetic insulators and study its scattering processes, tunneling conductance, and noise power by using an extended Bogoliubov-de Gennes scattering formalism. It is demonstrated that interedge coupling and noncollinear magnetizations allow for producing the usual and novel crossed Andreev reflections (ARs), respectively, and thus the corresponding spin-singlet and -triplet pairing entanglements. Moreover, by proper tuning of the band structures of the ferromagnetic layers, under the resonance bias voltage, not only perfect but also fully spin-polarized crossed AR at any magnetic orientational angle α is exhibited, which can be experimentally confirmed by the tunneling conductance and noise power. Particularly, the perfect and fully spin-polarized modulation between the spin-singlet and -triplet Andreev entanglements could be performed by α at certain energy values, which suggest that the setup can act as a topological superconducting spintronic device with such a manipulation function.

Nonequilibrium dynamical transition process between excited states of holographic superconductors

We study the dynamics of the holographic s-wave superconductors described by the Einstein-Maxwell-complex scalar field theory with a negative cosmological constant. If the eigenfunction of the linearized equation of motion of the scalar field in the planar RNAdS black hole background is chosen as the initial data, the bulk system will evolve to the intermediate state that corresponds to the excited state superconductor on the boundary. The process can be regarded as the non-equilibrium condensation process of the excited state of holographic superconductor. When the linear superposition of the eigenfunctions is chosen as the initial data, the system will go through a series of the intermediate states corresponding to different overtone numbers, which can be regarded as the dynamical transition process between the excited states of holographic superconductor. Because the intermediate states are metastable, the bulk system eventually evolves to the stationary state that corresponds the ground state of the holographic superconductor. We also provide a global and physical picture of the evolution dynamics of the black hole and the corresponding superconducting phase transition from the funneled landscape view, quantifying the weights of the states and characterizing the transitions and cascades towards the ground state.

Superconductivity in scandium borocarbide with orbital hybridization

Exploration of superconductivity in light element compounds has drawn considerable attention because those materials can easily realize the high T C superconductivity, such as LnNi2B2C (T C = 17 K), MgB2 (T C = 39 K), and very recently super-hydrides under pressure (T C = 250 K). Here we report the discovery of bulk superconductivity at 7.8 K in scandium borocarbide Sc20BC27 with a tetragonal lattice which structure changes based on the compound of Sc3C4 with very little B doping. Magnetization and specific heat measurements show bulk superconductivity. An upper critical field of H c2(0) ∼ 8 T is determined. Low temperature specific-heat shows that this system is a BCS fully gapped s-wave superconductor. Electronic structure calculations demonstrate that compared with Sc3C4 there are more orbital overlap and hybridization between Sc 3d electrons and 2p electrons of C-C(B)-C fragment in Sc20BC27, which form a new electric conduction path of Sc-C(B)-Sc. Those changes influence the band structure at the Fermi level and may be the reason of superconductivity in Sc20BC27.

Majorana Field Effect Transistor. Majorana Fermion Detection and Transport Properties

In this work we obtain analytically the transport properties as current and conductance in a toy model system formed by a quantum dot with a single level connected to a Kitaev chain deposited on a s-wave superconductor to identify the signature of Majorana zero modes (MZMs) called Majorana Fermions in solid state. For this, we use the Non-Equilibrium Green’s Functions (NEGF) also named as Keldysh formalism in the matrix form to obtain the current–voltage (I–V) and conductance– voltage (G–V) curves to which goes to characterize the investigated system. Thus, it’s possible to verify the presence of the Majorana Fermions in three points: (i) Conductance peak in zero polarization; (ii) The current difference depends on the asymmetry of μL and μR. We find that only for μL = μR, the source and drain currents are equal. (iii) The current difference depends on the asymmetry of ΓL and ΓR.

Holographic s-wave superconductors with conformal anomaly correction

We build a holographic s-wave conductor/superconductor model and an insulator/superconductor model in the four-dimensional conformal anomaly corrected (CAC) AdS gravity. The effects of CAC parameter $$\alpha $$ are studied using both numerical and analytical methods in the probe approximation. Concretely, when the CAC parameter increases, the critical temperature increases for the conductor/superconductor phase transition, while the critical chemical potential decreases for the insulator/superconductor case, which suggests that the increasing CAC parameter enhances both superconducting phase transitions. Meanwhile, below the critical temperature or beyond the critical chemical potential, the scalar hair begins to condense, and the condensed phases are found to be thermodynamically stable. The critical behaviors obtained from numerics are confirmed by our analytical analysis. In addition, the energy gap in the conductor/superconductor model decreases monotonically with the increasing CAC parameter.

Superconducting properties of the ternary boride YRh4B4

The low number of physical parameters for superconductivity has motivated researchers to perform bulk measurements in YRh4B4, discovered four decades ago, with superconducting transition temperature () of approximately 11 K. We performed electrical resistivity, magnetic susceptibility, and specific heat measurements to investigate the superconducting properties of the ternary borides YRh4B4 with CeCo4B4-type tetragonal structure. The nearly single-phase YRh4B4 had a moderately high of 10.6 K. The lower and upper critical fields were determined to be 1.5 and 32 kOe, respectively, by magnetic susceptibility and electrical resistivity measurements. The Ginzburg-Landau parameter was approximately 4.35, which is greater than , implying that YRh4B4 is a type-II superconductor. Because of specific heat measurements, the Debye temperature , , and 2 were determined to be 505 K, 1.56, and 3.91, respectively, where the specific heat jump at and the superconducting gap at 0 K are expressed by ΔC and . The electrical resistivity at low temperatures showed quadratic temperature dependence, and its coefficient A was determined to be 0.004426 µΩ· cm K−2, indicating a large density of states at Fermi energy. The electron-phonon coupling constant was derived to be 0.69. These results strongly suggest that YRh4B4 is a conventional s-wave superconductor described by the Bardeen–Cooper–Shriefer theory, and that the moderately high- in YRh4B4 is attributable to a high due to vibrations of boron with a light mass and a large A-value originating from the large density of states at Fermi energy. These results will facilitate microscopic investigations and provide clues to develop a novel high- metal superconductor.

Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator

By analytically solving the Bogoliubov–de Gennes equations we study the fermion bound states at the center of the core of a vortex in a two-dimensional superconductor. The superconducting states are induced via proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The strong spin–orbit coupling locks the spin perpendicular to the momentum (Rashba interaction). A zero-energy Majorana state arises together with an equally spaced () sequence of fermion excitations. The spin–momentum locking is key to the formation of the Majorana state. We present analytical expressions for the energy spectrum and the wave functions of the bound states. The wave functions fall off exponentially with the distance ρ from the core of the vortex as . An analytic expression for the local density of states (LDOS) for the bound states is obtained. The particle–hole symmetry is broken in the LDOS as a consequence of the spin–orbit coupling. The spin-polarization of the bound states is discussed. We also obtain the energy shifts of the bound states in a small magnetic field. A unitary transformation relating the model with Rashba interaction to the Dirac Hamiltonian is presented.

An analytic study on the excited states of holographic superconductors

Based on the Sturm-Liouville eigenvalue problem, we develop a general analytic technique to investigate the excited states of the holographic superconductors. By including more higher order terms in the expansion of the trial function, we observe that the analytic results agree well with the numeric data, which indicates that the Sturm-Liouville method is very powerful to study the holographic superconductors even if we consider the excited states. For both the holographic s-wave and p-wave models, we find that the excited state has a lower critical temperature than the corresponding ground state and the difference of the dimensionless critical chemical potential between the consecutive states is around 5. Moreover, we analytically confirm that the holographic superconductor phase transition with the excited states belongs to the second order, which can be used to back up the numerical findings for both s-wave and p-wave superconductors.

Charge density wave and superconductivity competition in Lu5Ir4Si10 : A proton irradiation study

Real-space modulated Charge Density Waves (CDW) are an ubiquituous feature in many families of superconductors. In particular, how CDW relates to superconductivity is an active and open question that has recently gathered much interest since CDWs have been discovered in many cuprates superconductors. Here we show that disorder induced by proton irradiation is a full-fledged tuning parameter that can bring essential information to answer this question as it affects CDW and superconductivity with different and unequivocal mechanisms. Specifically, in the model CDW superconductor Lu$_5$Ir$_4$Si$_{10}$ that develops a 1D CDW below 77\,K and s-wave superconductivity below 4\,K, we show that disorder enhances the superconducting critical temperature $T_\mathrm{c}$ and $H_\mathrm{c2}$ while it suppresses the CDW. Discussing how disorder affects both superconductivity and the CDW, we make a compelling case that superconductivity and CDW are competing for electronic density of states at the Fermi level in Lu$_5$Ir$_4$Si$_{10}$, and we reconcile the results obtained via the more common tuning parameters of pressure and doping. Owing to its prototypical, 1D, Peierls type CDW and the s-wave, weak-coupling nature of its superconductivity, this irradiation study of Lu$_5$Ir$_4$Si$_{10}$ provides the basis to understand and extend such studies to the more complex cases of density waves and superconductivity coexistence in heavy fermions, Fe-based or cuprates superconductors.

Dynamic pair-breaking current, critical superfluid velocity, and nonlinear electromagnetic response of nonequilibrium superconductors

We report numerical calculations of a dynamic pairbreaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude ac current density $J(t)=J_a\sin\Omega t$ with $\Omega$ well below the gap frequency $\Omega\ll \Delta_0/\hbar$. The dependencies $J_d(\Omega,T)$ and $v_d(\Omega,T)$ near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor and the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $\tau_{GL}$ and the inelastic electron-phonon relaxation time of quasiparticles $\tau_E$. We show that both approaches give similar frequency dependencies of $J_d(\Omega)$ and $v_d(\Omega)$ which gradually increase from their static pairbreaking GL values $J_c$ and $v_c$ at $\Omega\tau_E\ll 1$ to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at $\Omega\tau_E\gg 1$. Here $J_d$, $v_d$ and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed ac current and a fixed ac superfluid velocity induced by the applied ac magnetic field $H=H_a\sin\Omega t$ in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong ac current. It is shown that an ac current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as $\tau_E$ increases.

Unveiling Odd-Frequency Pairing around a Magnetic Impurity in a Superconductor.

We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Because of the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity, which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data.

Vortex bound state of a Kondo lattice coupled to a compensated metal

We theoretically study physical properties of the low-energy quasiparticle excitations at the vortex core in the full-gap superconducting state of the Kondo lattice coupled to compensated metals. Based on the mean-field description of the superconducting state, we numerically solve the Bogoliubov-de Gennes (BdG) equations for the tight-binding Hamiltonian. The isolated vortex is characterized by a length scale independent of the magnitude of the interaction and the energy level of the core bound state is the same order as the bulk gap. These properties are in strong contrast to the conventional s-wave superconductor. To gain further insights, we also consider the effective Hamiltonian in the continuous limit and construct the theoretical framework of the quasiclassical Green's function of conduction electrons. With the use of the Kramer-Pesch approximation, we analytically derive the spectral function describing the quasiparticle excitations which is consistent with the numerics. It has been revealed that the properties of the vortex bound state are closely connected to the characteristic odd frequency dependence of both the normal and anomalous self-energies which is proportional to the inverse of frequency.

Type-II Dirac Semimetal State in a Superconductor Tantalum Carbide**Supported by the National Natural Science Foundation of China (Grant Nos. 11974076, 11674369 and 11925408), and the Natural Science Foundation of Fujian Province of China (Grant No. 2018J06001), the Beijing Natural Science Foundation (Grant No. Z180008), Beijing Municipal Science and Technology Commission (Grant No. Z191100007219013), the National Key Research and Development Program

The exploration of topological Dirac semimetals with intrinsic superconductivity can be a most plausible way to discover topological superconductors. We propose that type-II Dirac semimetal states exist in the band structure of TaC, a well-known s-wave superconductor, by using the first-principles calculations and the k ⋅ p effective model. The tilted gapless Dirac cones, which are composed of Ta d and C p orbitals and are protected by C4v symmetry, are found to be below the Fermi level. The bands from Ta d orbitals are greatly coupled with the acoustic modes around the zone boundary, indicating their significant contribution to the superconductivity. The relatively high transition temperature ∼10.5 K is estimated to be consistent with the experimental data. To bring the type-II Dirac points close to chemical potential, hole doping is needed. This seems to decrease the transition temperature a lot, making the realization of topological superconductivity impossible.

Superconductivity in Weyl semimetals in a strong pseudomagnetic field

The superconducting s-wave state in Weyl semimetals in a strong strain-induced pseudomagnetic field is investigated in a model with local four-fermion interaction. It is found that only the inter-node pairing is possible in the lowest pseudo-Landau level approximation. Unlike the case of the lowest Landau level in a conventional magnetic field, the corresponding gap equation has only a trivial solution. Nevertheless, superconductivity can be induced via the proximity effect with a usual s-wave spin-singlet superconductor. Since a pseudomagnetic field is present necessarily at the surface of a Weyl semimetal, the proximity effect is strongly affected by the pseudomagnetic field. The analysis of such an effect showed that while no gap is opened in the spectrum, the degeneracy of energy levels is lifted. The unique character of the proximity effect in Weyl semimetals can be probed via the density of states, the spectral function, and the tunneling current. The density of states does not vanish at small energies and scales linearly with the pseudomagnetic field strength. This scaling is manifested also in the tunneling current.

Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators

Topological insulators, having intrinsic or proximity-coupled s-wave superconductivity, host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i)We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition is a surface phase transition after which MZMs appear. The second transition is the well-known vortex phase transition. We find that the surface transition appears because of the competition between the superconducting gap and the local T-breaking gap on the surface. (ii)We present numerical evidence that shows strong variation of the critical doping for the vortex phase transition as the center of the vortex is moved toward or away from the hinges of the sample. We believe our work provides new phenomenology that can help identify HOTIs, as well as illustrating a promising platform for the realization of MZMs.

Proximity-Induced Odd-Frequency Superconductivity in a Topological Insulator.

At an interface between a topological insulator (TI) and a conventional superconductor (SC), superconductivity has been predicted to change dramatically and exhibit novel correlations. In particular, the induced superconductivity by an s-wave SC in a TI can develop an order parameter with a p-wave component. Here we present experimental evidence for an unexpected proximity-induced novel superconducting state in a thin layer of the prototypical TI, Bi_{2}Se_{3} proximity coupled to Nb. From depth-resolved magnetic field measurements below the superconducting transition temperature of Nb, we observe a local enhancement of the magnetic field in Bi_{2}Se_{3} that exceeds the externally applied field, thus supporting the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state. Our experimental results are complemented by theoretical calculations supporting the appearance of such a component at the interface which extends into the TI. This state is topologically distinct from the conventional Bardeen-Cooper-Schrieffer state it originates from. To the best of our knowledge, these findings present a first observation of bulk odd-frequency superconductivity in a TI. We thus reaffirm the potential of the TI-SC interface as a versatile platform to produce novel superconducting states.

Bardasis-Schrieffer polaritons in excitonic insulators

Bardasis-Schrieffer modes in superconductors are fluctuations in subdominant pairing channels, e.g., d-wave fluctuations in an s-wave superconductor. This Rapid Communication shows that these modes also generically occur in excitonic insulators. In s-wave excitonic insulators, a p-wave Bardasis-Schrieffer mode exists below the gap energy, is optically active and hybridizes strongly with photons to form Bardasis-Schrieffer polaritons, which are observable in both far-field and near-field optical experiments.

Anomalous Josephson current in quantum anomalous Hall insulator-based superconducting junctions with a domain wall structure**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303301), the National Natural Science Foundation of China (Grant Nos. 11921005 and 11574007), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and Beijing Municipal Science & Technology Commission, China

We theoretically study the Josephson effect in a quantum anomalous Hall insulator (QAHI) nanoribbon with a domain wall structure and covered by the superconductor. The anomalous Josephson current, the nonzero supercurrent at the zero superconducting phase difference, appears with the nonzero magnetization and the suitable azimuth angle of the domain wall. Dependent on the configuration of the domain wall, the anomalous current peaks in the Bloch type but disappears in the Néel type because the y-component of magnetization is necessary to break symmetry to arouse the anomalous current. The phase shift of the anomalous current is tunable by the magnetization, the azimuth angle, or the thickness of the domain wall. By introducing a bare QAHI region in the middle of the junction which is not covered by the superconductor, the anomalous Josephson effect is enhanced such that the phase shift can exceed π. Thus, a continuous change between 0 and π junctions is realized via regulating the configuration of the domain wall or the magnetization strength. As long as an s-wave superconductor is placed on the top of the QAHI with a domain wall structure, this proposal can be experimentally fabricated and useful for the phase battery or superconducting quantum bit.

Holographic s-wave superconductors with Horndeski correction

Via both numerical and analytical methods, we build the holographic s-wave insulator/superconductor model in the five-dimensional AdS soliton with the Horndeski correction in the probe limit and study the effects of Horndeski parameter k on the superconductor model. For the fixed mass squared of the scalar field (m^2), the critical chemical potential mu _c increases with the larger Horndeski parameter k, which means that the increasing Horndeski correction hinders the superconductor phase transition. Meanwhile, above the critical chemical potential, the obvious pole arises in the low frequency of the imaginal part of conductivity, which signs the appearance of superconducting state. What is more, the energy of quasiparticle excitation decreases with the larger Horndeski correction. Furthermore, the critical exponent of the condensate (charge density) is frac{1}{2} (1), which is independent of the Horndeski correction. In addition, the analytical results agree well with the numerical results. Subsequently, the conductor/superconductor model with Horndeski correction is analytically realized in the four- and five-dimensional AdS black holes. It is observed that the increasing Horndeski correction decreases the critical temperature and thus hinders the superconductor phase transition, which agrees with the numerical result in the previous works.

Chiral Majorana fermions in graphene from proximity-induced superconductivity

We present a detailed theoretical study of chiral topological superconductor phases in proximity-superconducting graphene systems based on an effective model inspired by DFT simulations. Inducing s-wave superconductivity to quantum anomalous Hall effect systems leads to chiral topological superconductors. For out-of-plane magnetization we find topological superconducting phases with even numbers of chiral Majorana fermions per edge which is correlated to the opening of a nontrivial gap in the bulk system in the $\mathrm{ K}$-points and their connection under particle-hole symmetry. We show that in a quantum anomalous Hall insulator with in-plane magnetization and nontrivial gap opening at $\mathrm{M}$, the corresponding topological superconductor can be tuned to host only single chiral Majorana states at its edge which is promising for proposals exploiting such states for braiding operations.